Frontiers of Mathematics in China >

2015 , Vol. 10 >Issue 2: 303 - 321

DOI: https://doi.org/10.1007/s11464-015-0387-9

RESEARCH ARTICLE

Transportation inequalities for stochastic delay evolution equations driven by fractional Brownian motion

  • Zhi LI , 1 ,
  • Jiaowan LUO 2
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  • 1. School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
  • 2. School of Mathematics and Information, Guangzhou University, Guangzhou 510006, China

Received date: 26 Apr 2013

Accepted date: 05 May 2014

Published date: 12 Feb 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We discuss stochastic functional partial differential equations and neutral partial differential equations of retarded type driven by fractional Brownian motion with Hurst parameter H>1/2. Using the Girsanov transformation argument, we establish the quadratic transportation inequalities for the law of the mild solution of those equations driven by fractional Brownian motion under the L2 metric and the uniform metric.

Key words： Transportation inequality; Girsanov transformation; delay stochastic partial differential equation (SPDE); fractional Brownian motion (fBm)

Cite this article

Zhi LI , Jiaowan LUO . Transportation inequalities for stochastic delay evolution equations driven by fractional Brownian motion[J]. Frontiers of Mathematics in China, 2015 , 10(2) : 303 -321 . DOI: 10.1007/s11464-015-0387-9

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Bao J, Wang F Y, Yuan C. Transportation cost inequalities for neutral functional stochastic equations. arXiv: 1205.2184v1

2
Boufoussi B, Hajji S. Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space. Statist Probab Lett, 2010, 82: 1549-1558

DOI

3
Caraballo T, Garrido-Atienza M J, Taniguchi T. The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion. Nonlinear Anal, 2011, 74: 3671-3684

DOI

4
Da Prato G, Zabczyk J. Stochastic Equations in Infinite Dimensions. Cambridge: Cambridge University Press, 1992

DOI

5
Djellout H, Guillin A, Wu L. Transportation cost-information inequalities for random dynamical systems and diffusions. Ann Probab, 2004, 32: 2702-2732

DOI

6
Duncan T E, Maslowski B, Pasik-Duncan B. Stochastic equations in Hilbert space with a multiplicative fractional Gaussian noise. Stochastic Process Appl, 2005, 115: 1375-1383

DOI

7
Ma Y. Transportation inequalities for stochastic differential equations with jumps. Stochastic Process Appl, 2010, 120: 2-21

DOI

8
Pal S. Concentration for multidimensional diffusions and their boundary local times. Probab Theory Related Fields, 2012, 154: 225-254

DOI

9
Pazy A. Semigroup of linear operators and applications to partial differential equations. New York: Springer-Verlag, 1992

10
Saussereau B. Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion. Bernoulli, 2012, 18(1): 1-23

DOI

11
Üstünel A S. Transport cost inequalities for diffusions under uniform distance. Stoch Anal Related Topics, 2012, 22: 203-214

DOI

12
Wang F Y. Transportation cost inequalities on path spaces over Riemannian manifolds. Illinois J Math, 2002, 46: 1197-1206

13
Wang F Y. Probability distance inequalities on Riemannian manifolds and path spaces. J Funct Anal, 2004, 206: 167-190

DOI

14
Wu L. Transportation inequalities for stochastic differential equations of pure jumps. Ann Inst Henri Poincaré Probab Stat, 2010, 46: 465-479

DOI

15
Wu L, Zhang Z. Talagrand’s T2-transportation inequality w.r.t. a uniform metric for diffusions. Acta Math Appl Sin Engl Ser, 2004, 20: 357-364

DOI

16
Wu L, Zhang Z. Talagrand’s T2-transportation inequality and log-Sobolev inequality for dissipative SPDEs and applications to reaction-diffusion equations. Chin Ann Math Ser B, 2006, 27: 243-262

DOI

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